Half-BPS Wilson loop and AdS2/CFT1

Abstract

We study correlation functions of local operator insertions on the 1/2-BPS Wilson line in N = 4 super Yang-Mills theory. These correlation functions are constrained by the 1d superconformal symmetry preserved by the 1/2-BPS Wilson line and define a defect CFT 1 living on the line. At strong coupling, a set of elementary operator insertions with protected scaling dimensions correspond to fluctuations of the dual fundamental string in AdS 5 × S 5 ending on the line at the boundary and can be thought of as light fields propagating on the AdS 2 worldsheet. We use AdS/CFT techniques to compute the tree-level AdS 2 Witten diagrams describing the strong coupling limit of the fourpoint functions of the dual operator insertions. Using the OPE, we also extract the leading strong coupling corrections to the anomalous dimensions of the "two-particle" operators built out of elementary excitations. In the case of the circular Wilson loop, we match our results for the 4-point functions of a special type of scalar insertions to the prediction of localization to 2d Yang-Mills theory.

Non-supersymmetric Wilson loop in $$ \mathcal{N} $$ = 4 SYM and defect 1d CFT

“…This implies that strong-coupling dimensions of Φ 6 near the two conformal points should be (in agreement with [3,6])…”

“…discussed in the WML case [5,6]. In the latter case, correlators of local operators on the 1/2-BPS Wilson line have a OSp(4 * |4) 1d superconformal symmetry, while in the ordinary WL case one expects a non-supersymmetric "defect" CFT 1 with SO(3) × SO(6) "internal" symmetry.…”

“…It is of interest to relate the expression (2.67) to what is known about 2-point functions of (scalar) operators on the line or circle (see [3,5,6,[30][31][32][33][34]). Let us choose the scalar coupling in (1.1) to be along 6-th direction, i.e.…”

“…At strong coupling the "transverse" scalars Φ a should correspond to massless string coordinates y a in S 5 directions (with ∆ = ∆ + = 1, cf. (4.7)) [6] while Φ 6 should correspond [35] to the 2-particle world-sheet state y a y a (see section 4.2), with dimension ∆ = 2∆ + + O(…”

Minimal area surfaces in AdSn+1 and Wilson loops

“…The wavy Wilson line was originally studied by Semenoff and Young in [48] and greatly improved in [39], there has been renewed interest in this topic due to the possibility of defining a 1d conformal theory on the Wilson line [49,50]. In this section, we take the wavy line as an example of applying the formalism described in the previous sections.…”